Compute probability in urn with green returns
Urn Sampling with Specific Replacement Rules
You are presented with an urn containing colored balls. You will repeatedly draw one ball uniformly at random according to the following rules:
- If the drawn ball is green, it is immediately returned to the urn, and you continue drawing.
- If the drawn ball is red or blue, it is kept out of the urn.
- The process stops once you are holding three non-green balls.
Observation: The presence of green balls only affects the number of draws required to reach the stopping condition, not the possible colors of the three balls ultimately held.
Questions
- Case A: The urn initially contains 5 red, 5 blue, and 5 green balls. What is the probability that at least two of the three balls you are holding are red?
- Case B: The urn initially contains 10 red, 5 blue, and 5 green balls. First, provide an intuitive estimate for the probability that at least two of the three balls you are holding are red. Then, compute the exact probability.
AI interview prep
Core dilemma
The central engineering conflict is accurately modeling the system by correctly identifying and isolating the irrelevant components (green balls) to simplify the probability calculation, while ensuring the chosen statistical method precisely accounts for drawing without replacement from the relevant subset.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Compute probability in urn with green returns
Urn Sampling with Specific Replacement Rules
You are presented with an urn containing colored balls. You will repeatedly draw one ball uniformly at random according to the following rules:
- If the drawn ball is green, it is immediately returned to the urn, and you continue drawing.
- If the drawn ball is red or blue, it is kept out of the urn.
- The process stops once you are holding three non-green balls.
Observation: The presence of green balls only affects the number of draws required to reach the stopping condition, not the possible colors of the three balls ultimately held.
Questions
- Case A: The urn initially contains 5 red, 5 blue, and 5 green balls. What is the probability that at least two of the three balls you are holding are red?
- Case B: The urn initially contains 10 red, 5 blue, and 5 green balls. First, provide an intuitive estimate for the probability that at least two of the three balls you are holding are red. Then, compute the exact probability.